Stochastic fluctuations drive biological processes from particle diffusion to neuronal spike times. The goal of this talk is to use a variety of mathematical frameworks to understand such fluctuations and derive insight into the corresponding applications. We start by considering a novel stochastic process motivated by astrocytes, glial cells that ensheath neuronal synapses and can rapidly remove diffusing signaling molecules from the synaptic cleft. We generalize this setup to consider n diffusing particles that may leave a bounded domain by either ‘escaping’ through an absorbing boundary or being ‘captured’ by traps that must recharge  between captures. We prove that the number of captured particles grows on the order of log n because of this recharge time, which is drastically different than the linear growth observed for instantaneous recharging. We then generalize this framework further to investigate the celebrated formula of Berg and Purcell, which models the rate that cell surface receptors capture extracellular molecules, in the context of such recharging receptors. We end by exploring how the brain leverages interneuron diversity and noisy recurrent connections to assist with cortical computations. Specifically, we utilize a spatial model of the visual cortex and linear response theory to show how interneurons modulate the level of synchrony in visually induced gamma rhythms.